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Oscilloscopes
Measuring Power Using the DL750
While a commercial power meter offers convenience
and accuracy, and is the best approach to making
power measurements, an oscilloscope with
advanced mathematical calculation features offers
an alternative method. Such an oscilloscope is the
Yokogawa DL-750. While a commercial power meter
is the very best way to measure power, there are
instances where this equipment is unavailable, or
that an accurate approximation of power
consumption will suffice.
The following methodology is the same method
used in the commercial power analyzers and with
some caution; the DL750 can be used to calculate
power with impressive accuracy. The results in the
example below are comparable to those measured
using a Yokogawa WT230.
The DL750 is a digital sampling oscilloscope,
collecting many points of data. In the general sense
these are voltage points which can represent any
real world measurement, given the right sensor or
probe. Used correctly, the DL750 becomes a
powerful ally in custom RMS and power
measurements. The method for calculating any root
mean square or RMS value uses the following
expression:
The RMS for a discrete collection of n values {x1, x2,
x3, …, xn} is:
Assuming that enough samples are collected, a plot
of these points begins to approximate a continuous
function f(t), which we will examine over an interval
T1 ≤ t ≤ T2. and the equation for RMS is now defined
for a continuous waveform by:
The Yokogawa DL750 User Defined Math option
makes evaluation of such an equation very easy.
Calculations of power consumption always use RMS
measurements, specifically, the following three
expressions are applied to voltage and current
measurements:
Instantaneous Power = v(t)*i(t)
Apparent Power
Volt-Amps
=
Vrms*Irms,
with
units
of
Average Power = , sometimes called ‘Real Power’
with units of Watts and
Power Factor = (Average Power/Apparent Power),
as defined by the IEEE, and is unit-less.
Measuring Power Using the DL750
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Oscilloscopes
An everyday example of power measurement is that
of line power measurement. Often, it is necessary to
measure Average Power, Apparent Power, and
Power Factor. The following example illustrates the
specific steps needed in order to measure and
display current and voltage waveforms, calculate
Real and Apparent power.
The following example, which calculates the power
consumed by a linear power supply based on
measured waveforms - the voltage and current
waveforms are seen in in Figure 1. This is from a
DL750 screenshot. Notice that the Time/Div is 10 ms,
and displays exactly 6 cycles of the 60 Hertz
waveform.
Figure 1 Voltage and Current illustrating distorted current waveform
Measuring Power Using the DL750
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Oscilloscopes
In Figure 2, the same waveforms are visible with the
Time/Div later adjusted to 100ms/div in order to
display exactly 60 cycles of a 60 Hertz waveform.
This was chosen as a matter of convenience – and
the calculations defined below are carried-out upon
these 60 cycles. However, any convenient number
of cycles may be chosen and the results multiplied
appropriately to achieve a result that calculates
power over one second total time (since, Power =
Joules/Sec). The sampling rate should be adjusted
as appropriate, and in this example, it is 50 kS/s,
which is sufficient for these types of waveforms. Any
signal with a fast rise time, for example, will require
a higher sample rate.
Figure 2 Voltage, Current, Instantanaeous Power, and Integral Waveforms
Measuring Power Using the DL750
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Oscilloscopes
Figure 3 Power Factor
The DL750 User-Defined Math was set-up using
the following Equations:
Math1=C1*C2, representing Voltage*Current, or
instantaneous power, and can be seen as the 120
Hz. Waveform in the center of the D750 display in
Figure 2.
Math2=SQRT(INTG(C1*C1)*SQRT(INTG(C2*C2)),
which is the mathematical product of Vrms and
Irms, and can be seen as the diagonal line in the
center of the DL750 display in Figure 2.
In this calculation, T1=0 sec., and T2=1 sec. This
is simply the Frms equation illustrated above into
the DL750 User-Defined Math.
Math3=INTG(M1)/(SQRT(INTG(C1*C1)*SQRT
(INTG(C2*C2))), is the ratio of Real Power to
pparent Power, and this is the IEEE defintion of
Power Factor, and thus calculates Power Factor.
Place a MARKER from the CURSOR menu on
this to read the value at a valid point
(POSITION=0)
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Oscilloscopes
In the MEASURE menu, we take the following
parametric measurements:
Some tips, for good results when making power
measurements:
RMS(CH1) which is an RMS measurement of the
Voltage waveform, and the result can be observed
at the very bottom of the DL750 screen in Figure 2
as ‘Rms (Volt)’.
• Zero current probes regularly and de-magnetize
them before each use. This can be a frequent
source of errors, contributing a false DC current to
the current measurement. Particularly, Power
Factor is senstive to any error
• Use a sample rate that is appropriate for your
waveform. Any wave form with high-frequency
components (fast rise times) will need more
samples.
• Use Auto-Scaling within the MATH menu and
make sure that the waveforms do not “clip”,
introuducing erroneous measurements.
RMS(CH2) which is an RMS measurement of the
Current waveform, and the result can observed at
the very bottom of the DL750 screen in Figure 2
as ‘Rms (Curr)’.
Int2TY(Math1) sums the Real power. This
integral simply sums the real power, while
subtracting out the reactive power from the
instantaneous power equation. The result is REAL
Power and can be observed at the very bottom of
the DL750 screen in Figure 2 as ‘I2TY (Math).
Max (Math2) is used to determine the arithmetic
sum of the integral of instantaneous power over one
second and thus the Apparent Power Volt-Amps.
Each point in the equation (graphed as a diagonal
line) is the sum of the Volt-Amps. The sum after
one second is indicated by the very last point (to
the far right of the DL750 screen in the middle of
Figure 2.) Displayed as Max (Math)’ in Figure 2.
In the CURSOR menu, we take the following
parametric measurements:
Marker on Math3 at the midpoint.
Results:
The results of these measurements and calculations
using the DL750, in this example, were found to be:
Apparent Power = 37.92 Volt-Amps
Average Power = 31.54 Watts
Power Factor = 0.83
These results agreed quite closely (within 2%) with a
commercial power meter, the Yokogawa WT230:
Apparent Power = 38.51 VA
Average Power = 32.02
Power Factor = 0.83
Yokogawa Corporation of America
Test & Measurement Division
1.800.258.2552
Measuring Power Using the DL750
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